Lemma 3 (Lemma 3 in [1]}) 
Suppose the probability distribution of the \(n_N\)  random variables are multi-variant Gaussian, and \(\sup _{i, j \in \lbrace 1,\ldots , n_N\rbrace }|\rho _{ij}| \le M < 1\) , then for \(\mathcal {K} \subseteq \lbrace 1,\ldots ,n_N\rbrace  \backslash \lbrace i,j\rbrace \) ,
\(\sup _{(i,j, \mathcal {T}_{i,j}^m) \cup (i,j, \mathcal {T}_{i,j})} P(|Z_{ij \cdot \mathcal {K}} - z_{ij \cdot \mathcal {K}}| > \gamma ) \le O(N-n_N) \cdot \exp \Big ( (N-n_N-2)\log \frac{4-(\gamma /L)^2}{4+(\gamma /L)^2} \Big ),\) 
